Question

show that the tangent to the curve f:f(x)= x^2-x at the point p1(0,0) is perpendicular to the tangent to the curve at p2(1,0)

Answer 1

f ' (x) = 2x - 1
so at (0,0) slope = 2(0) -1 = -1
and at (1,0) slope = 2(1) - 1 = +1

since the slopes are negative reciprocals of each other the two tangents are perpendicular.